A Near-Optimal Best-of-Both-Worlds Algorithm for Online Learning with Feedback Graphs
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We consider online learning with feedback graphs, a sequential decision-making framework where the learner's feedback is determined by a directed graph over the action set. We present a computationally efficient algorithm for learning in this framework that simultaneously achieves near-optimal regret bounds in both stochastic and adversarial environments. The bound against oblivious adversaries is Õ (√(α T)), where T is the time horizon and α is the independence number of the feedback graph. The bound against stochastic environments is O( (ln T)^2 max_S∈ℐ(G)∑_i ∈ SΔ_i^-1) where ℐ(G) is the family of all independent sets in a suitably defined undirected version of the graph and Δ_i are the suboptimality gaps. The algorithm combines ideas from the EXP3++ algorithm for stochastic and adversarial bandits and the EXP3.G algorithm for feedback graphs with a novel exploration scheme. The scheme, which exploits the structure of the graph to reduce exploration, is key to obtain best-of-both-worlds guarantees with feedback graphs. We also extend our algorithm and results to a setting where the feedback graphs are allowed to change over time.
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